How to convert radians to degrees
Every radian is 57.2958 degrees, so the conversion is a single multiplication:
Worked example: 25 rad → 25 × 57.2958 = 1,432.4 °.
Quick mental estimate: Multiply by 57: 25 × 57 ≈ 1,425 ° (exact: 1,432.4).
Radians to degrees conversion table
| Radians (rad) | Degrees (°) |
|---|---|
| 1 rad | 57.2958 ° |
| 2 rad | 114.59 ° |
| 3 rad | 171.89 ° |
| 5 rad | 286.48 ° |
| 10 rad | 572.96 ° |
| 15 rad | 859.44 ° |
| 20 rad | 1,145.92 ° |
| 25 rad | 1,432.4 ° |
| 50 rad | 2,864.79 ° |
| 75 rad | 4,297.19 ° |
| 100 rad | 5,729.58 ° |
| 200 rad | 11,459.16 ° |
| 250 rad | 14,323.95 ° |
| 500 rad | 28,647.9 ° |
| 1,000 rad | 57,295.8 ° |
Values rounded to four decimals. For a value that is not in the table, use the converter above — it accepts decimals and negative numbers.
When you need this conversion
- Programming and spreadsheets: trigonometric functions almost always expect radians, while the value you have is usually in degrees.
- Engineering, surveying and CAD work, where drawings are annotated in degrees but calculations run in radians.
- Physics and mathematics coursework, where the two appear side by side in the same problem.
Getting it right
Spreadsheets and programming languages expect radians in their trigonometric functions. Feeding them a value in degrees returns a wrong answer silently, with no error message.
Spreadsheets and programming languages expect radians in their trigonometric functions, so a value in degrees has to be converted before use — no error is raised if you forget.
Sanity-check the direction of the result before you use it. One radian is 57.2958 degrees, so converting radians to degrees should make the number larger. If it moved the other way, the conversion was applied backwards — the reverse converter is one click away.
About the units
Radian (rad)
The radian is the angle at which the arc of a circle equals its radius. A full turn is 2π radians. Calculus, physics and most programming languages measure angles in radians.
Degree (°)
The degree is one 360th of a full turn. Compasses, protractors, geometry classes and everyday speech measure angles in degrees.
Frequently asked questions
How many degrees are in 1 radian?
1 radian equals 57.2958 degrees. To convert any value, multiply the number of radians by 57.2958.
How do I convert radians to degrees in my head?
Multiply by 57: 25 × 57 ≈ 1,425 ° (exact: 1,432.4).
Is the rad to ° conversion exact?
180° equals π radians exactly, so one radian is 180/π ≈ 57.2958°.
How do I convert radians to degrees in Excel or Google Sheets?
Put the value in A1 and use =A1*57.2958. Multiplying by the factor works in every spreadsheet, in any programming language, and on a basic calculator.
How many decimal places should I keep?
For everyday use two decimals are plenty. Keep four if the result feeds another calculation, and round only at the very end — rounding intermediate steps is the most common reason a result comes out slightly wrong.